1. Lacan’s Real, imaginary and Symbolic in Multiple Form Logic

Multiple Form Logic can be interpreted in terms of Jacques Lacan’s three realms of the “Real“, the “Imaginary” and the “Symbolic“. I.e. Reality is an External Space, located outside the Imaginary, as well as outside the Symbolic. The imaginary contains the symbolic, endlessly (re-)creating (inside its own space) Symbolic representations of the Real.

Slavoj Zizek‘s Lacanian philosophy is even closer to Laws of Form and Multiple Form Logic than Lacan’s. E.g. his view of “the subject”, or “Cartesian Cogito”, is a Distinction with Void content. Tony Myers describes it as follows:

For Zizek, Descartes‘s cogito is not the substantial ‘I’ of the individual, but an empty point of negativity. This empty point of negativity is not ‘nothing’ but the opposite of everything, or the negation of all determinacy. And it is exactly here, in this empty space devoid of all content, that Zizek locates the subject. The subject is, in other words, a void.

(Tony Myers, “Slavoj Zizek”, page 37)

I.e. the Cogito is an “empty point of negativity“, which is also “the opposite of everything”. This is consistent with the nature of brownian Distinctions or Multiple Forms, as negations. As an aside, since the nature of the imaginary is “the opposite of everything“, it follows that the opposite of the opposite of everything is everything. I.e.

2. A Lacan-Zizek interpretation of Logic implication in M.F. Logic

In Multiple Form Logic, logic implication is a configuration of Forms, where a (Symbolic) signifier is assigned (by the imagination) to a signified (Real) object. The Symbolic signifier is inside the boundary (of the Lacanian “imaginary”) and the Real (signified) is “out there”. The “implication operator” I, is the boundary of perception, i.e. the imagination itself:

The boundary of perception (or the Lacanian “imaginary”) I, contains the “premiss” P, as a Symbolic signifier of the Real “conclusion” R (object signified), which is “out there”.

So, Logic implication is (nothing but) the Act of perception, itself!

In the simplification of a composite Form that contains a cluster of such implications, it is often possible to progressively reduce the complexity of the composite form, through the elimination of anything Symbolic which corresponds precisely to something Real. To see how this is done, using the “axiom of perception” (axiom 3), we need to interpret axiom 3 from a Lacan / Zizek point of view:

3. A Lacan-Zizek interpretation of Multiple Form Logic’s Axiom 3

Seen in this light, the “Axiom of Perception” (axiom 3 of Multiple Form Logic) acquires an exact correspondence with Lacan’s and Zizek’s account of the Imaginary, the Real and the Symbolic:

“…if the Symbolic was not an incomplete or insufficient account of the Real, if, that is, we could apprehend the Real directly, then we, as subjects, would disappear. The reason for this is that if everything was exactly as it was meant to be, if everything could be grasped in its fullness, if there was no discrepancy between the way you saw the world and the way I saw it, if -in other words- every signifier perfectly matched every signified, and every sign matched every referent, there would be no signifying chain. All there would be is the Symbolic Order in perfect correspondence with the Real.”

(Tony Myers, “Slavoj Zizek”, page 28)

Axiom of Perception (click on the image for more)

Algebraically, all this is (verifiably) very true in Multiple Form Logic, too. In Multiple Form Logic, the imaginary is just a relative distinction, which is floating inside the Real. If this was ever to became identical with the (entirety of the) Real, then it would disappear! It exists, because it is relative; not absolute.

NOTE (for readers familiar with “Laws of Form“): This inherent relativity of Multiple Forms makes some of their algebraic properties very different from those of (absolute) Forms in “Laws of Form”.

The (Lacanian) “Symbolic” also consists of partial representations, or signifiers of “the Real” (=signified), selectively created within the space of “the Imaginary”. If these partial representations ever became identical to (the Totality of) “the Real” and if the imaginary also became identical to “the Real”, then everything (both imaginary and symbolic) would cancel out and dissappear!

Now, the fundamental distinction drawn by every (relative) being, is the Lacanian “imaginary”. We could say that the very existence of the Lacanian imaginary, as a boundary around its own (symbolic) space is the “first distinction drawn by Mind” – a distinction which Zizek identifies with “madness”, since it manifests initially as a void, or as a distinction with zero content:

It is this void that, for Zizek, enables the transition from a state of nature to a state of culture. This is because if there was no gap between a thing (or an object) and the representation of that thing (or word), then they would be identical and there would be no room for subjectivity. Words can only exist if we first ‘murder’ the thing, if we create a gap between them and the things they represent. This gap, the gap between nature and the beings immersed in it, is the subject. The subject, in other words, is the missing link, or ‘vanishing mediator’ as Zizek calls it, between the state of nature and the state of culture. Zizek’s point here is that the transition from nature to culture is not a story that can be told in terms of an evolutionary narrative, such as that offered by Hegel. Rather, the withdrawal-into-self which culminates in the cogito has to be presupposed as the vanishing mediator between the two, the missing link around which the transition is organized. In other words, Zizek reads this vanishing mediator as a passage through madness and, by so doing, he conceives the subject (which is the vanishing mediator) as mad. we have to ‘get rid’ of the Real before we can construct a substitute for it in the form of the Symbolic Order. Madness, therefore, is for Zizek a prerequisite for sanity, that is, for the ‘normalcy’ of a civilized subject.

(Tony Myers, “Slavoj Zizek”, page 37)

To ‘get rid of the Real’, in Multiple Form Logic, from an algebratic point of view, all we need to do is apply Axiom 3 in reverse: -Anything “Symbolic” (X) which corresponds precisely to something “Real” (X) out there, can indeed be “canceled out”, according to Axiom 3.

In the following image, the Signifier X corresponding to the Real object X can be “cancelled-out”:

See also:

4. The Divine Madness of the First Distinction and Slavoj Zizek

In a previous quote, Zizek’s view of the Imaginary as a “madness” which is also “the prerequisite of sanity” was mentioned. In reality, this is not so much an issue of “madness”, as much as an issue of a pre-logical cleavage of Being: A boundary that generates all the Laws of Logic, but pre-exists any Logic (as well as anything Symbolic). Nevertheless, perhaps the best possible account of such a (divine) madness is by Elytis, described in “the Consistency of Odysseus Elytis ‘Genesis’ with George Spencer Brown’s Laws of Form”.

@Marborchan
Yes, the signified (not only for Lacan) is typically part of the imaginary; not the Real. Also the Real is not exactly the same as Reality itself. These are crucial differences, but may be shown to be resolvable. First, because the primary relationship between imagination and reality does not preclude the internalisation of any (signified) object. The mind creates internal distinctions all the time, where both the signified and the signifier are internal. However, whenever there is a signifier-signified pair, another distinction is at work already, where signified is “outside” and signifier is “inside” the new distinction – which is internal, i.e. inside the imaginary.

All this should be clarified in a new post, where e.g. the projected “mirror image” of the self, is itself yet another “internal event”, in the inner part of the primary distinction, not inside the external reality.

All symbolic events are internal, after all; not magically occuring in Outer Reality but rationally created by the mind inside the mind. Every mental event is symbolic and everything symbolic is imaginary. However, this whole structure, instead of being created by gaps and distortions, it’s probably created by distinctions and forms, whose rational behaviour has most probably eluded Lacanian psychologists unaware of Laws of Form.